In design situations where a single solution must be selected, it is often desirable to present the designer with a smart Pareto set of solutions-a minimal set of nondominated solutions that sufficiently represents the tradeoff characteristics of the design space.These sets are generally created by finding many well-distributed solutions and then either filtering out the excess ones or searching more closely in those regions that appear to have significant tradeoff. Such methods suffer from the inherent inefficiency of creating numerous solutions that will never be presented to the designer. This paper introduces the Smart Normal Constraint (SNC) method-a Pareto set generation method capable of directly generating a smart Pareto set. Direct generation is achieved by iteratively updating an approximation of the design space geometry and searching only in those regions capable of yielding new smart Pareto solutions. This process is made possible through the use of a new, computationally benign calculation for identifying regions of high tradeoff in a design space. Examples are provided that show the SNC method performing significantly more efficiently than the predominant existing method for generating smart Pareto sets.

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Formulation space exploration is a new strategy for multiobjective optimization that facilitates both divergent exploration and convergent optimization during the early stages of design. The formulation space is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into the formulation space, the solution to an optimization problem is no longer predefined by any single problem formulation, as it is with traditional optimization methods. Instead, a designer is free to change, modify, and update design objectives, variables, and constraints and explore design alternatives without requiring a concrete understanding of the design problem a priori. To facilitate this process, we introduce a new vector/matrix-based definition for multiobjective optimization problems, which is dynamic in nature and easily modified. Additionally, we provide a set of exploration metrics to help guide designers while exploring the formulation space. Finally, we provide an example to illustrate the use of this new, dynamic approach to multiobjective optimization.

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